Properties

Label 1960.2.a
Level 19601960
Weight 22
Character orbit 1960.a
Rep. character χ1960(1,)\chi_{1960}(1,\cdot)
Character field Q\Q
Dimension 4141
Newform subspaces 2525
Sturm bound 672672
Trace bound 1111

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 1960=23572 1960 = 2^{3} \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1960.a (trivial)
Character field: Q\Q
Newform subspaces: 25 25
Sturm bound: 672672
Trace bound: 1111
Distinguishing TpT_p: 33, 1111, 1313

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ0(1960))M_{2}(\Gamma_0(1960)).

Total New Old
Modular forms 368 41 327
Cusp forms 305 41 264
Eisenstein series 63 0 63

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

225577FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++++44445539393737553232770077
++++--47476641413939663333880088
++-++-48487741414040773333880088
++--++45453342423737333434880088
-++++-48484444444040443636880088
-++-++45456639393737663131880088
--++++44444440403636443232880088
----47476641413939663333880088
Plus space++178178181816016014714718181291293131003131
Minus space-190190232316716715815823231351353232003232

Trace form

41q+4q3q5+33q9+2q1314q17+8q19+4q23+41q25+16q27+2q29+24q3124q332q37+8q39+2q41+8q43+3q4520q47++112q99+O(q100) 41 q + 4 q^{3} - q^{5} + 33 q^{9} + 2 q^{13} - 14 q^{17} + 8 q^{19} + 4 q^{23} + 41 q^{25} + 16 q^{27} + 2 q^{29} + 24 q^{31} - 24 q^{33} - 2 q^{37} + 8 q^{39} + 2 q^{41} + 8 q^{43} + 3 q^{45} - 20 q^{47}+ \cdots + 112 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ0(1960))S_{2}^{\mathrm{new}}(\Gamma_0(1960)) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces A-L signs Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7} 2 5 7
1960.2.a.a 1960.a 1.a 11 15.65115.651 Q\Q None 280.2.q.c 00 2-2 1-1 00 - ++ ++ SU(2)\mathrm{SU}(2) q2q3q5+q9q113q13+q-2q^{3}-q^{5}+q^{9}-q^{11}-3q^{13}+\cdots
1960.2.a.b 1960.a 1.a 11 15.65115.651 Q\Q None 1960.2.a.b 00 2-2 1-1 00 - ++ - SU(2)\mathrm{SU}(2) q2q3q5+q9+4q112q13+q-2q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots
1960.2.a.c 1960.a 1.a 11 15.65115.651 Q\Q None 280.2.q.b 00 1-1 1-1 00 ++ ++ ++ SU(2)\mathrm{SU}(2) qq3q52q92q11+4q13+q-q^{3}-q^{5}-2q^{9}-2q^{11}+4q^{13}+\cdots
1960.2.a.d 1960.a 1.a 11 15.65115.651 Q\Q None 1960.2.a.d 00 1-1 11 00 - - - SU(2)\mathrm{SU}(2) qq3+q52q95q117q13+q-q^{3}+q^{5}-2q^{9}-5q^{11}-7q^{13}+\cdots
1960.2.a.e 1960.a 1.a 11 15.65115.651 Q\Q None 280.2.q.a 00 1-1 11 00 - - - SU(2)\mathrm{SU}(2) qq3+q52q9+2q11q15+q-q^{3}+q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots
1960.2.a.f 1960.a 1.a 11 15.65115.651 Q\Q None 1960.2.a.f 00 1-1 11 00 ++ - - SU(2)\mathrm{SU}(2) qq3+q52q9+3q11+q13+q-q^{3}+q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots
1960.2.a.g 1960.a 1.a 11 15.65115.651 Q\Q None 40.2.a.a 00 00 1-1 00 ++ ++ - SU(2)\mathrm{SU}(2) qq53q9+4q11+2q132q17+q-q^{5}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots
1960.2.a.h 1960.a 1.a 11 15.65115.651 Q\Q None 1960.2.a.d 00 11 1-1 00 - ++ - SU(2)\mathrm{SU}(2) q+q3q52q95q11+7q13+q+q^{3}-q^{5}-2q^{9}-5q^{11}+7q^{13}+\cdots
1960.2.a.i 1960.a 1.a 11 15.65115.651 Q\Q None 280.2.q.a 00 11 1-1 00 - ++ ++ SU(2)\mathrm{SU}(2) q+q3q52q9+2q11q15+q+q^{3}-q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots
1960.2.a.j 1960.a 1.a 11 15.65115.651 Q\Q None 1960.2.a.f 00 11 1-1 00 ++ ++ - SU(2)\mathrm{SU}(2) q+q3q52q9+3q11q13+q+q^{3}-q^{5}-2q^{9}+3q^{11}-q^{13}+\cdots
1960.2.a.k 1960.a 1.a 11 15.65115.651 Q\Q None 280.2.a.b 00 11 11 00 ++ - - SU(2)\mathrm{SU}(2) q+q3+q52q95q11q13+q+q^{3}+q^{5}-2q^{9}-5q^{11}-q^{13}+\cdots
1960.2.a.l 1960.a 1.a 11 15.65115.651 Q\Q None 280.2.q.b 00 11 11 00 ++ - - SU(2)\mathrm{SU}(2) q+q3+q52q92q114q13+q+q^{3}+q^{5}-2q^{9}-2q^{11}-4q^{13}+\cdots
1960.2.a.m 1960.a 1.a 11 15.65115.651 Q\Q None 280.2.q.c 00 22 11 00 - - - SU(2)\mathrm{SU}(2) q+2q3+q5+q9q11+3q13+q+2q^{3}+q^{5}+q^{9}-q^{11}+3q^{13}+\cdots
1960.2.a.n 1960.a 1.a 11 15.65115.651 Q\Q None 1960.2.a.b 00 22 11 00 - - - SU(2)\mathrm{SU}(2) q+2q3+q5+q9+4q11+2q13+q+2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots
1960.2.a.o 1960.a 1.a 11 15.65115.651 Q\Q None 280.2.a.a 00 33 1-1 00 ++ ++ - SU(2)\mathrm{SU}(2) q+3q3q5+6q95q11+5q13+q+3q^{3}-q^{5}+6q^{9}-5q^{11}+5q^{13}+\cdots
1960.2.a.p 1960.a 1.a 22 15.65115.651 Q(2)\Q(\sqrt{2}) None 280.2.q.d 00 2-2 22 00 - - ++ SU(2)\mathrm{SU}(2) q+(1+β)q3+q52βq9+(2+)q11+q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-2+\cdots)q^{11}+\cdots
1960.2.a.q 1960.a 1.a 22 15.65115.651 Q(2)\Q(\sqrt{2}) None 1960.2.a.q 00 2-2 22 00 - - ++ SU(2)\mathrm{SU}(2) q+(1+β)q3+q52βq9q11+q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}-q^{11}+\cdots
1960.2.a.r 1960.a 1.a 22 15.65115.651 Q(17)\Q(\sqrt{17}) None 280.2.a.d 00 1-1 2-2 00 - ++ - SU(2)\mathrm{SU}(2) qβq3q5+(1+β)q9βq11+(2+)q13+q-\beta q^{3}-q^{5}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots
1960.2.a.s 1960.a 1.a 22 15.65115.651 Q(33)\Q(\sqrt{33}) None 280.2.a.c 00 11 22 00 - - - SU(2)\mathrm{SU}(2) q+βq3+q5+(5+β)q9+(4β)q11+q+\beta q^{3}+q^{5}+(5+\beta )q^{9}+(4-\beta )q^{11}+\cdots
1960.2.a.t 1960.a 1.a 22 15.65115.651 Q(2)\Q(\sqrt{2}) None 280.2.q.d 00 22 2-2 00 - ++ - SU(2)\mathrm{SU}(2) q+(1+β)q3q5+2βq9+(22β)q11+q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots
1960.2.a.u 1960.a 1.a 22 15.65115.651 Q(2)\Q(\sqrt{2}) None 1960.2.a.q 00 22 2-2 00 - ++ ++ SU(2)\mathrm{SU}(2) q+(1+β)q3q5+2βq9q11+(1+)q13+q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots
1960.2.a.v 1960.a 1.a 33 15.65115.651 3.3.1944.1 None 280.2.q.e 00 00 3-3 00 ++ ++ - SU(2)\mathrm{SU}(2) q+β1q3q5+(3+β1+β2)q9+(1+)q11+q+\beta _{1}q^{3}-q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots
1960.2.a.w 1960.a 1.a 33 15.65115.651 3.3.1944.1 None 280.2.q.e 00 00 33 00 ++ - ++ SU(2)\mathrm{SU}(2) qβ1q3+q5+(3+β1+β2)q9+(1+)q11+q-\beta _{1}q^{3}+q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots
1960.2.a.x 1960.a 1.a 44 15.65115.651 4.4.16448.2 None 1960.2.a.x 00 2-2 4-4 00 ++ ++ ++ SU(2)\mathrm{SU}(2) qβ1q3q5+(1+β1+β2)q9+(β1+)q11+q-\beta _{1}q^{3}-q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots
1960.2.a.y 1960.a 1.a 44 15.65115.651 4.4.16448.2 None 1960.2.a.x 00 22 44 00 ++ - ++ SU(2)\mathrm{SU}(2) q+β1q3+q5+(1+β1+β2)q9+(β1+)q11+q+\beta _{1}q^{3}+q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots

Decomposition of S2old(Γ0(1960))S_{2}^{\mathrm{old}}(\Gamma_0(1960)) into lower level spaces

S2old(Γ0(1960)) S_{2}^{\mathrm{old}}(\Gamma_0(1960)) \simeq S2new(Γ0(14))S_{2}^{\mathrm{new}}(\Gamma_0(14))12^{\oplus 12}\oplusS2new(Γ0(20))S_{2}^{\mathrm{new}}(\Gamma_0(20))6^{\oplus 6}\oplusS2new(Γ0(35))S_{2}^{\mathrm{new}}(\Gamma_0(35))8^{\oplus 8}\oplusS2new(Γ0(40))S_{2}^{\mathrm{new}}(\Gamma_0(40))3^{\oplus 3}\oplusS2new(Γ0(49))S_{2}^{\mathrm{new}}(\Gamma_0(49))8^{\oplus 8}\oplusS2new(Γ0(56))S_{2}^{\mathrm{new}}(\Gamma_0(56))4^{\oplus 4}\oplusS2new(Γ0(70))S_{2}^{\mathrm{new}}(\Gamma_0(70))6^{\oplus 6}\oplusS2new(Γ0(98))S_{2}^{\mathrm{new}}(\Gamma_0(98))6^{\oplus 6}\oplusS2new(Γ0(140))S_{2}^{\mathrm{new}}(\Gamma_0(140))4^{\oplus 4}\oplusS2new(Γ0(196))S_{2}^{\mathrm{new}}(\Gamma_0(196))4^{\oplus 4}\oplusS2new(Γ0(245))S_{2}^{\mathrm{new}}(\Gamma_0(245))4^{\oplus 4}\oplusS2new(Γ0(280))S_{2}^{\mathrm{new}}(\Gamma_0(280))2^{\oplus 2}\oplusS2new(Γ0(392))S_{2}^{\mathrm{new}}(\Gamma_0(392))2^{\oplus 2}\oplusS2new(Γ0(490))S_{2}^{\mathrm{new}}(\Gamma_0(490))3^{\oplus 3}\oplusS2new(Γ0(980))S_{2}^{\mathrm{new}}(\Gamma_0(980))2^{\oplus 2}